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That's not a critical flaw. In metaphysics, you can't take for granted that the world is not in your head. The only thing you really can do is to find an inconsistency, if you want to prove someone wrong.
Langan has no problems convincing me. His attempt at constructing a reality theory is serious and mature and I think he conducts his business about the way an ordinary person with such aims would. He's not a literary genius like Robert Pirsig, he's just really smart otherwise.
I've never heard anyone to present such criticism of the CTMU that would actually imply understanding of what Langan is trying to do. The CTMU has a mistake. It's that Langan believes (p. 49) the CTMU to satisfy the Law Without Law condition, which states: "Concisely, nothing can be taken as given when it comes to cosmogony." (p. 8)
According to the Mind Equals Reality Principle, the CTMU is comprehensive. This principle "makes the syntax of this theory comprehensive by ensuring that nothing which can be cognitively or perceptually recognized as a part of reality is excluded for want of syntax". (p. 15) But undefinable concepts can neither be proven to exist nor proven not to exist. This means the Mind Equals Reality Principle must be assumed as an axiom. But to do so would violate the Law Without Law condition.
The Metaphysical Autology Principle could be stated as an axiom, which would entail the nonexistence of undefinable concepts. This principle "tautologically renders this syntax closed or self-contained in the definitive, descriptive and interpretational senses". (p. 15) But it would be arbitrary to have such an axiom, and the CTMU would again fail to fulfill Law Without Law.
If that makes the CTMU rubbish, then Russell's Principia Mathematica is also rubbish, because it has a similar problem which was pointed out by Gödel. EDIT: Actually the problem is somewhat different than the one addressed by Gödel.
Langan's paper can be found here EDIT: Fixed link.
To clarify, I'm not the generic "skeptic" of philosophical thought experiments. I am not at all doubting the existence of the world outside my head. I am just an apparently competent metaphysician in the sense that I require a Wheeler-style reality theory to actually be a Wheeler-style reality theory with respect to not having arbitrary declarations.
There might not be many people here to who are sufficiently up to speed on philosophical metaphysics to have any idea what a Wheeler-style reality theory, for example, is. My stereotypical notion is that the people at LW have been pretty much ignoring philosophy that isn't grounded in mathematics, physics or cognitive science from Kant onwards, and won't bother with stuff that doesn't seem readable from this viewpoint. The tricky thing that would help would be to somehow translate the philosopher-speak into lesswronger-speak. Unfortunately this'd require some fluency in both.
It's not like your average "competent metaphysicist" would understand Langan either. He wouldn't possibly even understand Wheeler. Langan's undoing is to have the goals of a metaphysicist and the methods of a computer scientist. He is trying to construct a metaphysical theory which structurally resebles a programming language with dynamic type checking, as opposed to static typing. Now, metaphysicists do not tend to construct such theories, and computer scientists do not tend to be very familiar with metaphysics. Metaphysical theories tend to be deterministic instead of recursive, and have a finite preset amount of states that an object can have. I find the CTMU paper a bit sketchy and missing important content besides having the mistake. If you're interested in the mathematical structure of a recursive metaphysical theory, here's one: http://www.moq.fi/?p=242
Formal RP doesn't require metaphysical background knowledge. The point is that because the theory includes a cycle of emergence, represented by the power set function, any state of the cycle can be defined in relation to other states and prior cycles, and the amount of possible states is infinite. The power set function will generate a staggering amount of information in just a few cycles, though. Set R is supposed to contain sensory input and thus solve the symbol grounding problem.
Of course the symbol grounding problem is rather important, so it doesn't really suffice to say that "set R is supposed to contain sensory input". The metaphysical idea of RP is something to the effect of the following:
Let n be 4.
R contains everything that could be used to ground the meaning of symbols.
N contains relations of purely abstract symbols.
Let ℘(T) be the power set of T.
The solving of the symbol grounding problem requires R and N to be connected. Let us assume that ℘(Rn) ⊆ Rn+1. R5 hasn't been defined, though. If we don't assume subsets of R to emerge from each other, we'll have to construct a lot more complicated theories that are more difficult to understand.
This way we can assume there are two ways of connecting R and N. One is to connect them in the same order, and one in the inverse order. The former is set O and the latter is set S.
O set includes the "realistic" theories, which assume the existence of an "objective reality".
The relationship between O and N:
S set includes "solipsistic" ideas in which "mind focuses to itself".
The relationship between S and N:
That's the metaphysical portion in a nutshell. I hope someone was interested!
We were talking about applying the metaphysics system to making an AI earlier in IRC, and the symbol grounding problem came up there as a basic difficulty in binding formal reasoning systems to real-time actions. It doesn't look like this was mentioned here before.
I'm assuming I'd want to actually build an AI that needs to deal with symbol grounding, that is, it needs to usefully match some manner of declarative knowledge it represents in its internal state to the perceptions it receives from the outside world and to the actions it performs on it. Given this, I'm getting almost no notion of what useful work this theory would do for me.
Mathematical descriptions can be useful for people, but it's not given that they do useful work for actually implementing things. I can define a self-improving friendly general artificial intelligence mathematically by defining
FAI = <S, P*>as an artificial intelligence instance, consisting of its current internal state S and the history of its perceptions up to the present P*,a: FAI -> A*as a function that gives the list of possible actions for a given FAI instanceu: A -> Realas a function that gives the utility of each action as a real number, with higher numbers given to actions that advance the purposes of the FAI better based on its current state and perception history andf: FAI * A -> S, Pas an update function that takes an action and returns a new FAI internal state with any possible self-modifications involved in the action applied, and a new perception item that contains whatever new observations the FAI made as a direct result of its action.And there's a quite complete mathematical description of a friendly artificial intelligence, you could probably even write a bit of neat pseudocode using the pieces there, but that's still not likely to land me a cushy job supervising the rapid implementation of the design at SIAI, since I don't have anything that does actual work there. All I did was push all the complexity into the black boxes of the
u,aandf.I also implied a computational approach where the system enumerates every possible action, evaluates them all and then picks a winner with how I decided to split up the definition. This is mathematically expedient, given that in mathematics any concerns of computation time can be pretty much waved off, but appears rather naive computationally, as it is likely that both coming up with possible actions and evaluating them can get extremely expensive in the artificial general intelligence domain.
With the metaphysics thing, beyond not getting a sense of it doing any work, I'm not even seeing where the work would hide. I'm not seeing black box functions that need to do an unknowable amount of work, just sets with strange elements being connected to other sets with strange elements. What should you be able to do with this thing?
You probably have a much more grassroot-level understanding of the symbol grounding problem. I have only solved the symbol grounding problem to the extent that I have formal understanding of its nature.
In any case, I am probably approaching AI from a point of view that is far from the symbol grounding problem. My theory does not need to be seen as an useful solution to that problem. But when an useful solution is created, I postulate it can be placed within RP. Such a solution would have to be an algorithm for creating S-type or O-type sets of members of R.
More generally, I would find RP to be useful as an extremely general framework of how AI or parts of AI can be constructed in relation to each other, ecspecially with regards to understanding lanugage and the notion of consciousness. This doesn't necessarily have anything to do with some more atomistic AI projects, such as trying to make a robot vacuum cleaner find its way back to the charging dock.
At some point, philosophical questions and AI will collide. Suppose the following thought experiment:
We have managed to create such a sophisticated brain scanner, that it can tell whether a person is thinking of a cat or not. Someone is put into the machine, and the machine outputs that the person is not thinking of a cat. The person objects and says that he is thinking of a cat. What will the observing AI make of that inconsistency? What part of the observation is broken and results in nonconformity of the whole?
In order to solve this problem, the AI may have to be able to conceptualize the fact that the brain scanner is a deterministic machine which simply accepts X as input and outputs Y. The scanner does not understand the information it is processing, and the act of processing information does not alter its structure. But the person is different.
RP should help with such problems because it is intended as an elegant, compact and flexible way of defining recursion while allowing the solution of the symbol grounding problem to be contained in the definition in a nontrivial way. That is, RP as a framework of AI is not something that says: "Okay, this here is RP. Just perform the function RP(sensory input) and it works, voilá." Instead, it manages to express two different ways of solving the symbol grounding problem and to define their accuracy as a natural number n. In addition, many emergence relations in RP are logical consequences of the way RP solves the symbol grounding problem (or, if you prefer, "categorizes the parts of the actual solution to the symbol grounding problem").
In the previous thought experiment, the AI should manage to understand that the scanner deterministically performs the operation ℘(R) ⊆ S, and does not define S in terms of anything else. The person, on the other hand, is someone whose information processing is based on RP or something similar.
But what you read from moq.fi is something we wrote just a few days ago. It is by no means complete.
Questions to you:
I will not guarantee having discussions with me is useful for attaining a good job. ;)
I don't really understand this part.
"The scanner does not understand the information but the person does" sounds like some variant of Searle's Chinese Room argument when presented without further qualifiers. People in AI tend to regard Searle as a confused distraction.
The intelligent agent model still deals with deterministic machines that take input and produce output, but it incorporates the possibility of changing the agent's internal state by presenting the output function as just taking the entire input history X* as an input to the function that produces the latest output Y, so that a different history of inputs can lead to a different output on the latest input, just like it can with humans and more sophisticated machines.
I suppose the idea here is that there is some difference whether there is a human being sitting in the scanner, or, say, a toy robot with a state of two bits where one is I am thinking about cats and the other is I am broken and will lie about thinking about cats. With the robot, we could just check the "broken" bit as well from the scan when the robot is disagreeing with the scanner, and if it is set, conclude that the robot is broken.
I'm not seeing how humans must be fundamentally different. The scanner can already do the extremely difficult task of mapping a raw brain state to the act of thinking about a cat, it should also be able to tell from the brain state whether the person has something going on in their brain that will make them deny thinking about a cat. Things being deterministic and predictable from knowing their initial state doesn't mean they can't have complex behavior reacting to a long history of sensory inputs accompanied by a large amount of internal processing that might correspond quite well to what we think of as reflection or understanding.
Sorry I keep skipping over your formalism stuff, but I'm still not really grasping the underlying assumptions behind this approach. (The underlying approach in the computer science approach are, roughly, "the physical world exists, and is made of lots of interacting, simple, Turing-computable stuff and nothing else", "animals and humans are just clever robots made of the stuff", "magical souls aren't involved, not even if they wear a paper bag that says 'conscious experience' on their head")
The whole philosophical theory of everything thing does remind me of this strange thing from a year ago, where the building blocks for the theory were made out of nowadays more fashionable category theory rather than set theory though.
I've read some of this Universal Induction article. It seems to operate from flawed premises.
Suppose the brain uses algorithms. An uncontroversial supposition. From a computational point of view, the former citation is like saying: "In order for a computer to not run a program, such as Indiana Jones and the Fate of Atlantis, the computer must be executing some command to the effect of "DoNotExecuteProgram('IndianaJonesAndTheFateOfAtlantis')".
That's not how computers operate. They just don't run the program. They don't need a special process for not running the program. Instead, not running the program is "implicitly contained" in the state of affairs that the computer is not running it. But this notion of implicit containment makes no sense for the computer. There are infinitely many programs the computer is not running at a given moment, so it can't process the state of affairs that it is not running any of them.
Likewise, the use of an implicit bias towards simplicity cannot be meaningfully conceptualized by humans. In order to know how this bias simplifies everything, one would have to know, what information regarding "everything" is omitted by the bias. But if we knew that, the bias would not exist in the sense the author intends it to exist.
Furthermore:
The author says that there are variations of the no free lunch theorem for particular contexts. But he goes on to generalize that the notion of no free lunch theorem means something independent of context. What could that possibly be? Also, such notions as "arbitrary complexity" or "randomness" seem intuitively meaningful, but what is their context?
The problem is, if there is no context, the solution cannot be proven to address the problem of induction. But if there is a context, it addresses the problem of induction only within that context. Then philosophers will say that the context was arbitrary, and formulate the problem again in another context where previous results will not apply.
In a way, this makes the problem of induction seem like a waste of time. But the real problem is about formalizing the notion of context in such a way, that it becomes possible to identify ambiguous assumptions about context. That would be what separates scientific thought from poetry. In science, ambiguity is not desired and should therefore be identified. But philosophers tend to place little emphasis on this, and rather spend time dwelling on problems they should, in my opinion, recognize as unsolvable due to ambiguity of context.
The omitted information in this approach is information with a high Kolmogorov complexity, which is omitted in favor of information with low Kolmogorov complexity. A very rough analogy would be to describe humans as having a bias towards ideas expressible in few words of English in favor of ideas that need many words of English to express. Using Kolmogorov complexity for sequence prediction instead of English language for ideas in the construction gets rid of the very many problems of rigor involved in the latter, but the basic idea is pretty much the same. You look into things that are briefly expressible in favor of things that must be expressed in length. The information isn't permanently omitted, it's just depriorized. The algorithm doesn't start looking at the stuff you need long sentences to describe before it has convinced itself that there are no short sentences that describe the observations it wants to explain in a satisfactory way.
One bit of context that is assumed is that the surrounding universe is somewhat amenable to being Kolmogorov-compressed. That is, there are some recurring regularities that you can begin to discover. The term "lawful universe" sometimes thrown around in LW probably refers to something similar.
Solomonoff's universal induction would not work in a completely chaotic universe, where there are no regularities for Kolmogorov compression to latch on. You'd also be unlikely to find any sort of native intelligent entities in such universes. I'm not sure if this means that the Solomonoff approach is philosophically untenable, but needing to have some discoverable regularities to begin with before discovering regularities with induction becomes possible doesn't strike me as that great a requirement.
If the problem of context is about exactly where you draw the data for the sequence which you will then try to predict with Solomonoff induction, in a lawless universe you wouldn't be able to infer things no matter which simple instrumentation you picked, while in a lawful universe you could pick all sorts of instruments, tracking the change of light during time, tracking temperature, tracking the luminousity of the Moon, for simple examples, and you'd start getting Kolmogorov-compressible data where the induction system could start figuring repeating periods.
The core thing "independent of context" in all this is that all the universal induction systems are reduced to basically taking a series of numbers as input, and trying to develop an efficient predictor for what the next number will be. The argument in the paper is that this construction is basically sufficient for all the interesting things an induction solution could do, and that all the various real-world cases where induction is needed can be basically reduced into such a system by describing the instrumentation which turns real-world input into a time series of numbers.
Okay. In this case, the article does seem to begin to make sense. Its connection to the problem of induction is perhaps rather thin. The idea of using low Kolmogorov complexity as justification for an inductive argument cannot be deduced as a theorem of something that's "surely true", whatever that might mean. And if it were taken as an axiom, philosophers would say: "That's not an axiom. That's the conclusion of an inductive argument you made! You are begging the question!"
However, it seems like advancements in computation theory have made people able to do at least remotely practical stuff on areas, that bear resemblance to more inert philosophical ponderings. That's good, and this article might even be used as justification for my theory RP - given that the use of Kolmogorov complexity is accepted. I was not familiar with the concept of Kolmogorov complexity despite having heard of it a few times, but my intuitive goal was to minimize the theory's Kolmogorov complexity by removing arbitrary declarations and favoring symmetry.
I would say, that there are many ways of solving the problem of induction. Whether a theory is a solution to the problem of induction depends on whether it covers the entire scope of the problem. I would say this article covers half of the scope. The rest is not covered, to my knowledge, by anyone else than Robert Pirsig and experts of Buddhism, but these writings are very difficult to approach analytically. Regrettably, I am still unable to publish the relativizability article, which is intended to succeed in the analytic approach.
In any case, even though the widely rejected "statistical relevance" and this "Kolmogorov complexity relevance" share the same flaw, if presented as an explanation of inductive justification, the approach is interesting. Perhaps, even, this paper should be titled: "A Formalization of Occam's Razor Principle". Because that's what it surely seems to be. And I think it's actually an achievement to formalize that principle - an achievement more than sufficient to justify the writing of the article.
At first, I didn't quite understand this. But I'm reading Introduction to Automata Theory, Languages and Computation. Are you using the * in the same sense here as it is used in the following UNIX-style regular expression?
This expression is intended to refer to all word that begin with a capital letter and do not contain any surprising characters such as ö or -. Examples: "Jennifer", "Washington", "Terminator". The * means [a-z] may have an arbitrary amount of iterations.
Yeah, that's probably where it comes from. The [A-Z] can be read as "the set of every possible English capital letter" just like X can be read as "the set of every possible perception to an agent", and the * denotes some ordered sequence of elements from the set exactly the same way in both cases.
I don't find the Chinese room argument related to our work - besides, it seems to possibly vaguely try to state that what we are doing can't be done. What I meant is that AI should be able to:
Failure to understand this could make the robot naively both take machines apart and cut peoples brains in order to experimentally verify, which approach produces better results. Of course there are also other things to consider when the robot tries to figure out what to do.
I don't consider robots and humans fundamentally different. If the AI were complex enough to understand the aforementioned things, it also would understand the notion that someone wants to take it apart and reprogam it, and could consent or object.
The latter has, to my knowledge, never been done. Arguably, the latter task requires different ability which the scanner may not have. The former requires acquiring a bitmap and using image recognition. It has already been done with simple images such as parallel black and white lines, but I don't know whether bitmaps or image recognition were involved in that. If the cat is a problem, let's simplify the image to the black and white lines.
Even the simplest entities, such as irrational numbers or cellular automata, can have complex behavior. Humans, too, could be deterministic and predictable given that the one analyzing a human has enough data and computing power. But RP is about the understanding a consciousness could attain of itself. Such an understanding could not be deterministic within the viewpoint of that consciousness. That would be like trying to have a map contain itself. Every iteration of the map representing itself needs also to be included in the map, resulting in a requirement that the map should contain an infinite amount of information. Only an external observer could make a finite map, but that's not what I had in mind when beginning this RP project. I do consider the goals of RP somehow relevant to AI, because I don't suppose it's ok a robot cannot conceptualize its own thought very elaborately, if it were intended to be as much human as possible, and maybe even be able to write novels.
I am interested in the ability to genuinely understand the worldviews of other people. For example, the gap between scientific and religious people. In the extreme, these people think of each other in such a derogatory way, that it would be as if they would view each other as having failed the Turing test. I would like robots to understand also the goals and values of religious people.
Well, that's supposed to be a good thing, because there are supposed to be none. But saying that might not help. If you don't know what consciousness or the experience of reality mean in my use (perhaps because you would reduce such experiences to theoretical models of physical entities and states of neural networks), you will probably not understand what I'm doing. That would suggest you cannot conceptualize idealistic ontology or you believe "mind" to refer to an empty set.
I see here the danger for rather trivial debates, such as whether I believe an AI could "experience" consciousness or reality. I don't know what such a question would even mean. I am interested of whether it can conceptualize them in ways a human could.
The CTMU also states something to the effect of this. In that case, Langan is making a mistake, because he believes the CTMU to be a Wheeler-style reality theory, which contradicts the earlier statement. In your case, I guess it's just an opinion, and I don't feel a need to say you should believe otherwise. But I suppose I can present a rather cogent argument against that within a few days. The argument would be in the language of formal logic, so you should be able to understand it. Stay tuned...
I don't wish to be unpolite, but I consider these topics boring and obvious. Hopefully I haven't missed anything important when making this judgement.
Your strange link is very intriguing. I like very much being given this kind of links. Thank you.
About the classification thing: Agree that it's very important that a general AI be able to classify entities into "dumb machines" and things complex enough to be self-aware, warrant an intentional stance and require ethical consideration. Even putting aside the ethical concerns, being able to recognize complex agents with intentions and model their intentions instead of their most likely massively complex physical machinery is probably vital to any sort of meaningful ability to act in a social domain with many other complex agents (cf. Dennett's intentional stance)
I understood the existing image reconstruction experiments measure the activation on the visual cortex when the subject is actually viewing an image, which does indeed get you a straightforward mapping to a bitmap. This isn't the same as thinking about a cat, a person could be thinking about a cat while not looking at one, and they could have a cat in their visual field while daydreaming or suffering from hysterical blindness, so that they weren't thinking about a cat despite having a cat image correctly show up in their visual cortex scan.
I don't actually know what the neural correlate of thinking about a cat, as opposed to having one's visual cortex activated by looking at one, would be like, but I was assuming interpreting it would require much more sophisticated understanding of the brain, basically at the level of difficult of telling whether a brain scan correlates with thinking about freedom, a theory of gravity or reciprocality. Basically something that's entirely beyond current neuroscience and more indicative of some sort of Laplace's demon like thought experiment where you can actually observe and understand the whole mechanical ensemble of the brain.
Quines are maps that contain themselves. A quining system could reflect on its entire static structure, though it would have to run some sort of emulation slower than its physical substrate to predict its future states. Hofstadter's GEB links quines to reflection in AI.
"There aren't any assumptions" is just a plain non-starter. There's the natural language we're using that's used to present the theory and ground the concepts in the theory, and natural language basically carries a billion years of evolution leading to the three billion base pair human genome loaded with accidental complexity, leading to something from ten to a hundred thousand years of human cultural evolution with even more accidental complexity that probably gets us something in the ballpark of 100 megabytes irreducible complexity from the human DNA that you need to build up a newborn brain and another 100 megabytes (going by the heuristic of one bit of permanently learned knowledge per one second) for the kernel of the cultural stuff a human needs to learn from their perceptions to be able to competently deal with concepts like "income tax" or "calculus". You get both of those for free when talking with other people, and neither when trying to build an AGI-grade theory of the mind.
This is also why I spelled out the trivial basic assumptions I'm working from (and probably did a very poor job at actually conveying the whole idea complex). When you start doing set theory, I assume we're dealing with things at the complexity of mathematical objects. Then you throw in something like "anthropology" as an element in a set, and I, still in math mode, start going, whaa, you need humans before you have anthropology, and you need the billion years of evolution leading to the accidental complexity in humans to have humans, and you need physics to have the humans live and run the societies for anthropology to study, and you need the rest of the biosphere for the humans to not just curl up and die in the featureless vacuum and, and.. and that's a lot of math. While the actual system with the power sets looks just like uniform, featureless soup to me. Sure, there are all the labels, which make my brain do the above i-don't-get-it dance, but the thing I'm actually looking for is the mathematical structure. And that's just really simple, nowhere near what you'd need to model a loose cloud of hydrogen floating in empty space, not to mention something many orders of magnitude more complex like a society of human beings.
My confusion about the assumptions is basically that I get the sense that analytic philosophers seem to operate like they could just write the name of some complex human concept, like "morality", then throw in some math notation like modal logic, quantified formulas and set memberships, and call it a day. But what I'm expecting is something that teaches me how to program a computer to do mind-stuff, and a computer won't have the corresponding mental concept for the word "morality" like a human has, since the human has the ~200M special sauce kernel which gives them that. And I hardly ever see philosophers talking about this bit.
A theory of mind that can actually do the work needs to build up the same sort of kernel evolution and culture have set up for people. For the human ballpark estimate, you'd have to fill something like 100 000 pages with math, all setting up the basic machinery you need for the mind to get going. A very abstracted out theory of mind could no doubt cut off an order of magnitude or two out of that, but something like Maxwell's equations on a single sheet of paper won't do. It isn't answering the question of how you'd tell a computer how to be a mind, and that's the question I keep looking at this stuff with.
There are many ways to answer that question. I have a flowchart and formulae. The opposite of that would be something to the effect of having the source code. I'm not sure why you expect me to have that. Was it something I said?
I thought I've given you links to my actual work, but I can't find them. Did I forget? Hmm...
If you dislike metaphysics, only the latter is for you. I can't paste the content, because the formatting on this website apparently does not permit html formulae. Wait a second, it does permit formulae, but only LaTeX. I know LaTeX, but the formulae aren't in that format right now. I should maybe convert them.
You won't understand the flowchart if you don't want to discuss metaphysics. I don't think I can prove that something, of which you don't know what it is, could be useful to you. You would have to know what it is and judge for yourself. If you don't want to know, it's ok.
I am currently not sure why you would want to discuss this thing at all, given that you do not seem quite interested of the formalisms, but you do not seem interested of metaphysics either. You seem to expect me to explain this stuff to you in terms of something that is familiar to you, yet you don't seem very interested to have a discussion where I would actually do that. If you don't know why you are having this discussion, maybe you would like to do something else?
There are quite probably others in LessWrong who would be interested of this, because there has been prior discussion of CTMU. People interested in fringe theories, unfortunately, are not always the brightest of the lot, and I respect your abilities to casually namedrop a bunch of things I will probably spend days thinking about.
But I don't know why you wrote so much about billions of years, babies, human cultural evolution, 100 megabytes and such. I am troubled by the thought that you might think I'm some loony hippie who actually needs a recap on those things. I am not yet feeling very comfortable in this forum because I perceive myself as vulnerable to being misrepresented as some sort of a fool by people who don't understand what I'm doing.
I'm not trying to change LessWrong. But if this forum has people criticizing the CTMU without having a clue of what it is, then I attain a certain feeling of entitlement. You can't just go badmouthing people and their theories and not expect any consequences if you are mistaken. You don't need to defend yourself either, because I'm here to tell you what recursive metaphysical theories such as the CTMU are about, or recommend you to shut up about the CTMU if you are not interested of metaphysics. I'm not here to bloat my ego by portraying other people as fools with witty rhetoric, and if you Google about the CTMU, you'll find a lot of people doing precisely that to the CTMU, and you will understand why I fear that I, too, could be treated in such a way.
You want a sweater. I give you a baby sheep, and it is the only baby sheep you have ever seen that is not completely lame or retarded. You need wool to produce the sweater, so why are you disappointed? Look, the mathematical part of the theory is something we wrote less than a week ago, and it is already better than any theory of this type I have ever heard of (three or four). The point is not that this would be excruciatingly difficult. The point is that for some reason, almost nobody is doing this. It probably has something to do with the severe stagnation in the field of philosophy. The people who could develop philosophy find the academic discipline so revolting they don't.
I did not come to LessWrong to tell everyone I have solved the secrets of the universe, or that I am very smart. My ineptitude in math is the greatest single obstacle in my attempts to continue development. If I didn't know exactly one person who is good at math and wants to do this kind of work with me, I might be in an insane asylum, but no more about that. I came here because this is my life... and even though I greatly value the MOQ community, everyone on those mailing lists is apparently even less proficient in maths and logic as I am. Maybe someone here thinks this is fun and wants to have a fun creative process with me.
I would like to write a few of those 100 000 pages that we need. I don't get your point. You seem to require me to have written them before I have written them.
Do you expect to build the digital sauce kernel without any kind of a plan - not even a tentative one? If not, a few pages of extremely abstract formulae is all I have now, and frankly, I'm not happy about that either. I can't teach you nearly anything you seem interested of, but I could really use some discussion with interested people. And you have already been helpful. You don't need to consider me someone who is aggressively imposing his views on individual people. I would love to find people who are interested of these things because there are so few of them.
I had a hard time figuring out what you mean by basic assumptions, because I've been doing this for such a long time I tend to forget what kind of metaphysical assumptions are generally held by people who like science but are disinterested of metaphysics. I think I've now caught up with you. Here are some basic assumptions.
I have read GEB but don't remember much. I'll recap what a quine is. I tend to need to discuss mathematical things with someone face to face before I understand them, which slows down progress.
The cat/line thing is not very relevant, but apparently I didn't remember the experiment right. However, if the person and the robot could not see the lines at the same time for some reason - such as the robot needing to operate the scanner and thus not seeing inside the scanner - the robot could alter the person's brain to produce a very strong response to parallel lines in order to verify that the screen inside the scanner, which displays the lines, does not malfunction, is not unplugged, the person is not blind, etc. There could be more efficient ways of finding such things out, but if the robot has replaceable hardware and can thus live indefinitely, it has all the time in the world...
According to the abstract, the scope of the theory you linked is a subset of RP. :D I find this hilarious because the theory was described as "ridiculously broad". It seems to attempt to encompass all of O, and may contain interesting insight my work clearly does not contain. But the RP defines a certain scope of things, and everything in this article seems to belong to O, with perhaps some N without clearly differentiating the two. S is missing, which is rather usual in science. From the scientific point of view, it may be hard to understand what Buddhists could conceivably believe to achieve by meditation. They have practiced it for millenia, yet they did not do brain scans that would have revealed its beneficial effects, and they did not perform questionnaires either and compile the results into a statistic. But they believed it is good to meditate, and were not very interested of knowing why it is good. That belongs to the realm of S.
In any case, this illustrates an essential feature of RP. It's not so much a theory about "things", you know, cars, flowers, finances, than a theory about what are the most basic kind of things, or about what kind of options for the scope of any theory or statement are intelligible. It doesn't currently do much more because the algorith part is missing. It's also not necessarily perfect or anything like that. If something apparently coherent cannot be included to the scope of RP in a way that makes sense, maybe the theory needs to be revised.
Perhaps I could give a weird link in return. This is written by someone who is currently a Professor of Analytic Philosophy at the University of Melbourne. I find the theory to mathematically outperform that of Langan in that it actually has mathematical content instead of some sort of a sketch. The writer expresses himself coherently and appears to understand in what style do people expect to read that kind of text. But the theory does not recurse in interesting ways. It seems quite naive and simple to me and ignores the symbol grounding problem. It is practically an N-type theory, which only allegedly has S or O content. The writer also seems to make exagerrating interpretations of what Nagarjuna said. These exagerrating interpretations lead to making the same assumptions which are the root of the contradiction in CTMU, but The Structure of Emptiness is not described as a Wheeler-style reality theory, so in that paper, the assumptions do not lead to a contradiction although they still seem to misunderstand Nagarjuna.
By the way, I have thought about your way of asking for basic assumptions. I guess I initially confused it with you asking for some sort of axioms, but since you weren't interested of the formalisms, I didn't understand what you wanted. But now I have the impression that you asked me to make general statements of what the theory can do that are readily understood from the O viewpoint, and I think it has been an interesting approach for me, because I didn't use that in the MOQ community, which would have been unlikely to request that approach.
I'll address the rest in a bit, but about the notation:
T -> Uis a function from set T to set U.P*means a list of elements in set P, where the difference from set is that elements in a list are in a specific order.The notation as a whole was a somewhat fudged version of intelligent agent formalism. The idea is to set up a skeleton for modeling any sort of intelligent entity, based on the idea that the entity only learns things from its surroundings though a series of perceptions, which might for example be a series of matrices corresponding to the images a robot's eye camera sees, and can only affect its surroundings by choosing an action it is capable of, such as moving a robotic arm or displaying text to a terminal.
The agent model is pretty all-encompassing, but also not that useful except as the very first starting point, since all of the difficulty is in the exact details of the function that turns the most likely massive amount of data in the perception history into a well-chosen action that efficiently furthers the goals of the AI.
Modeling AIs as the function from a history of perceptions to an action is also related to thought experiments like Ned Block's Blockhead, where a trivial AI that passes the Turing test with flying colors is constructed by merely enumerating every possible partial conversation up to a certain length, and writing up the response a human would make at that point of that conversation.
Scott Aaronson's Why philosophers should care about computational complexity proposes to augment the usual high-level mathematical frameworks with some limits to the complexity of the black box functions, to make the framework reject cases like Blockhead, which seem to be very different from what we'd like to have when we're looking for a computable function that implements an AI.